CP Violation In Tau Decays

1. CP Violation In Tau Decays Nita Sinha The Institute of Mathematical Sciences Chennai

2. CPV in Charged Leptons • CP violation has been observed in K meson and B meson decays • and perhaps (?) recently even in the D meson decays • SM cannot produce the observed matter vs antimatter asymmetry • Look elsewhere—Neutrinos • Charged leptons • Electric Dipole Moments • Will hopefully simultaneously be able to pin down the kind • of New Physics

3. BABAR Rapid Communications PRD 85, 031102 (2012) Search for CP violation in the decay The BaBar collaboration reported a measurement of a rate asymmetry in this tau decay mode • Naively one would not expect any CPV in this decay mode • as there is no weak phase involved. • However, - mix t: (VtsV*td)2 ~ 10, mt2 c: (VcsV*cd)2 ~ 2, mc2 u: (VusV*ud)2 ~ 2, mu2 c dominates

4. Asymmetry from Neutral Kaon Mixing In the presence of CPV, the observed neutral Kaon states of definite mass and lifetime are: In the limit of CP conservation and reduce to CP eigenstates, > =|> , where Bigi and Sanda estimated the asymmetry in the SM due to mixing to be-- The observed asymmetry has the opposite sign!

5. Sign of the Asymmetry In fact, the sign of such an CP asymmetry expected to be opposite to the CP Asymmetry in charged D decays

6. Careful Analysis The measured CP asymmetry has the opposite sign to the theoretical expectation, leading to a ~2.8 Babar has done a rather careful analysis—including corrections pointed out by theorists: 1

7. 2 The discrepancy from expectation (if confirmed with higher statistical significance) needs to be explained

8. Why is this interesting? • Except for neutral K mixing, tau decays can only be affected by • Direct CPV • CP asymmetries in semi-hadronic final states can probe both CPV • comingfrom New hadronic and leptonic physics. • Once the well measured Kaon oscillation contribution to CP • asymmetry is accounted for, any further deviations provide • clean signals of New Physics

9. Decay Rate The differential decay rate for may be written as: In Standard Model Where, the leptonic term: and the hadronic term is given in terms of the hadronic vector current which is parameterized in terms of scalar and vector form factors as: Kpi system will only allow and

10. ) is the momentum of Kaon in hadron rest frame No Vector –Scalar Interference term Form Factors parameterized in terms of Briet -Wigner forms with energy dependent widths l=1 p wave vector state l=0 s wave scalar state

11. are complex coefficients for the relative contributions of the other Resonances wrtthe dominant contribution. Fits to data, possible by using and OR and

13. CP Asymmetry • Note: • For CP asymmetry need strong and weak phases • Strong phase-provided by the resonances! • No Weak phase in SM, can come from New Physics • (complex coupling) ) is the ratio of NSI amp. to SM amp CP asymmetry being linear in NP has higher sensitivity to it than effects like lfv or edms

14. Additional Scalar Interaction (Charged Higgs) ? • Naively expect a charged scalar boson to provide the additional • NSI amplitude, • With a complex weak coupling and strong phase difference of • scalar and vector FF • CP Asymmetry BUT • For charged Higgs, no new FF, only modification, so calculable • Interference of scalar and vector FF term vanishes after the • angular integration, so cannot give the decay rate asymmetry • although can give asymmetry in distributions • The Vector contribution being odd under parity, interference of • vector-scalar is odd, hence vanishes when integrated over the • full (parity even) phase space

15. Belle and Cleo Analysis

16. Other Options-Tensor interaction? Complex coupling NP amplitude Hadronic Current

17. This interference survives even after full phase space integration, as both vector and tensor terms are odd under parity

18. Numerical estimates of NP Parameters • Use the observed BR and ACP to determine the coupling strength of this new tensor interaction and its CP violating phase. • Small coupling will not affect the fits to BR, as it will appeared squared, yet its linear interference term will be sufficient to generate the asymmetry. • Strong phases determined from the complex form of the form factors (vector and scalar) and Case I

20. Case II and

21. Future • Hadronic form factors for tensor contribution could be estimated from • lattice calculations • Larger data sample could be analyzed by the experimental groups, including fits with tensorial contribution • Some handle on tensor form factor can pin down the coupling strength and weak phase further. • Note that the dependence of tensor mod-squared term is quite different from other terms which will enable its extraction from data.

22. Summary • KM Mechanism of CPV verified, explains all measured CPV • BAU requires larger CPV • Explore the lepton sector– Neutrinos • Charged leptons • Other possible sources of CPV and NP need to be explored • Observation of a CP asymmetry in the tau decay mode is interesting and if the • deviation from the expected SM value confirmedat higher statistical significance • It will be an excellent probe of NP • In a model independent way we explored the possibility if tensor interactions could • possibly explain the observed asymmetry.

23. Thank You